Subgroups — #1307×C₁₅₁ #34064639

Order 19328.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#432×C₁₅₁	C₂	1	2	yes	maximal
2	#423×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₁₅₁	C₄	1	2	yes	—
4	C₂×C₄²×C₁₅₁	C₂²	1	1	yes	characteristic
5	C₄⋊C₈×C₁₅₁	—	2	2	no	—
6	C₄⋊C₈×C₁₅₁	—	2	2	no	—
7	C₂²⋊C₈×C₁₅₁	C₄	1	4	yes	—
8	#97×C₁₅₁	—	2	2	no	—
9	C₂²×C₄×C₁₅₁	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₁₅₁	C₂×C₄	1	2	yes	—
11	M₁₆×C₁₅₁	—	4	2	no	—
12	C₂×C₈×C₁₅₁	—	2	4	no	—
13	C₂×C₈×C₁₅₁	—	2	2	no	—
14	C₄²×C₁₅₁	D₄	1	1	yes	characteristic
15	C₄²×C₁₅₁	D₄	1	2	yes	—
16	C₄²×C₁₅₁	Q₈	1	1	yes	characteristic
17	C₂³×C₁₅₁	C₄²	1	1	yes	characteristic
18	C₂×C₄×C₁₅₁	—	2	1	no	—
19	C₂×C₄×C₁₅₁	—	2	1	no	—
20	C₂×C₄×C₁₅₁	—	4	2	no	—
21	C₂×C₄×C₁₅₁	C₂²⋊C₄	1	2	yes	—
22	C₂×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₅₁	C₄⋊C₄	1	2	yes	—
25	C₈×C₁₅₁	—	4	4	no	—
26	C₈×C₁₅₁	—	4	2	no	—
27	C₂²×C₁₅₁	—	2	1	no	—
28	C₂²×C₁₅₁	—	2	2	no	—
29	C₂²×C₁₅₁	#95	1	1	yes	characteristic
30	C₄×C₁₅₁	—	2	1	no	—
31	C₄×C₁₅₁	—	2	2	no	—
32	C₄×C₁₅₁	—	2	2	no	—
33	C₄×C₁₅₁	#100	1	1	yes	characteristic
34	C₄×C₁₅₁	#101	1	1	yes	characteristic
35	C₂×C₁₅₁	—	4	1	no	—
36	C₂×C₁₅₁	#343	1	1	yes	characteristic
37	C₂×C₁₅₁	#344	1	2	yes	—
38	C₁₅₁	#1307	1	1	yes	characteristic, direct product factor, Sylow
39	#1307	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	#432	C₂×C₁₅₁	1	2	yes	—
41	#423	C₂×C₁₅₁	1	1	yes	characteristic
42	C₂×M₁₆	C₄×C₁₅₁	1	2	yes	—
43	C₂×C₄²	C₂²×C₁₅₁	1	1	yes	characteristic
44	C₄⋊C₈	—	2	2	no	—
45	C₄⋊C₈	—	2	2	no	—
46	C₂²⋊C₈	C₄×C₁₅₁	1	4	yes	—
47	#97	—	2	2	no	—
48	C₂²×C₄	C₂×C₄×C₁₅₁	1	1	yes	characteristic
49	C₂²×C₄	C₂×C₄×C₁₅₁	1	2	yes	—
50	M₁₆	—	4	2	no	—
51	C₂×C₈	—	2	4	no	—
52	C₂×C₈	—	2	2	no	—
53	C₄²	D₄×C₁₅₁	1	1	yes	characteristic
54	C₄²	D₄×C₁₅₁	1	2	yes	—
55	C₄²	Q₈×C₁₅₁	1	1	yes	characteristic
56	C₂³	C₄²×C₁₅₁	1	1	yes	characteristic
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	C₂²⋊C₄×C₁₅₁	1	2	yes	—
61	C₂×C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
62	C₂×C₄	C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
63	C₂×C₄	C₄⋊C₄×C₁₅₁	1	2	yes	—
64	C₈	—	4	4	no	—
65	C₈	—	4	2	no	—
66	C₂²	—	2	1	no	—
67	C₂²	—	2	2	no	—
68	C₂²	#95×C₁₅₁	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	2	2	no	—
71	C₄	—	2	2	no	—
72	C₄	#100×C₁₅₁	1	1	yes	characteristic
73	C₄	#101×C₁₅₁	1	1	yes	characteristic
74	C₂	—	4	1	no	—
75	C₂	#343×C₁₅₁	1	1	yes	characteristic
76	C₂	#344×C₁₅₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₅₁	#95
commutator	C₂³	C₄²×C₁₅₁
Frattini, cosocle	C₂×C₄²	C₂²×C₁₅₁
prime radical	C₂³×C₁₅₁	C₄²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₅₁ ◁ C₂×C₄²×C₁₅₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
38. C₁₅₁	#1307	direct (N × H)
39. #1307	C₁₅₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#432×C₁₅₁	2
#423×C₁₅₁	2
#1307	151

Subgroups — #1307×C151 #34064639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1307×C₁₅₁ #34064639